The first thing you need to know is that the NT doesn't pass through Missoula. You need to head south from the Whitefish/C-Falls area. (Hope you are not skipping an out and back to Glacier N.P.) There are several ways to do that. Whatever you do, don't take Hwy 206 south from C-Falls. No shoulder and lots of really fast traffic. ACA's Great Parks North route connects Whitefish/C-Falls to Missoula.
I highly recommend Wayfarers State Park in Bigfork. It's one of the state parks that has the special hiker/biker sites with all sorts of nice amenities, like a bear locker, covered picnic table, tent pads and electrical outlets. Whitefish Lake State Park, on the NT, is another one. Drop your gear then head into Whitefish for groceries/food. Both have no-turn-away policies if crowded.
There are a few USFS campgrounds in the Seely Lake area. Or you can camp behind the motor lodge at the north end of town. (There are showers.) Owners are very nice. You'll see it on your left as you hit the business area of town.
If you want to to push on, Salmon Lake State Park on MT 83 south of Seeley Lake is yet another of the state parks that has the hiker/biker sites described above' although I have never stayed there. Note that MT 83 loses its shoulder for a while south of town. I recommend hitting the road early if you stay in the Seeley Lake area. The shoulder picks up again before you hit MT 200 at Clearwater Jct.
The walk down to Kootenai Falls west of Libby, MT, is well worth it. Before you get there, on MT 56, Dorr Skeels is a great little USFS campground. Water, but no shower. The site next to the day use picnic area has a great view of the lake.
https://www.fs.usda.gov/recarea/kootenai/recreation/camping-cabins/recarea/?recid=49912&actid=29The fired chicken at the bar/restaurant in Rexford, MT, is out of this world. (It's not the battered kind.) You'll be hungry after riding MT 47 up from Libby.
The federal campground there (Rexford Bench) is large. No showers, but the bar/restaurant will sell you a shower.
